Software alignment of the LHCb outer tracker chambers [Elektronische Ressource] / presented by Marc Deissenroth

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DISSERTATIONsubmitted to theCombined Faculties for the Natural Sciences and Mathematicsof the Ruperto-Carola University of Heidelberg, Germanyfor the degree ofdoctor rerum naturaliumpresented byDipl.-Phys. Marc Deissenrothborn in Salzkotten, GermanystOral examination: April 21 , 2010Software Alignment ofthe LHCb Outer Tracker ChambersReferees: Prof. Dr. Ulrich UwerProf. Dr. Hans-Christian Schultz-CoulonAbstractThis work presents an alignment algorithm that was developed to precisely deter-mine the positions of the LHCb Outer Tracker detector elements. The algorithmis based on the reconstruction of tracks and exploits that misalignments of thedetector change the residual between a measured hit and the reconstructed track.It considers di erent levels of granularities of the Outer Tracker geometry and fullyaccounts for correlations of all elements which are imposed by particle trajectories.In extensive tests, simulated shifts and rotations for di erent levels of the detectorgranularity have been used as input to the track reconstruction and alignmentprocedure. With about 260 000 tracks the misalignments are recovered with astatistical precision ofO(10 100m) for the translational degrees of freedom and2 1ofO(10 10 mrad) for rotations. A study has been performed to determinethe impact of Outer Tracker misalignments on the performance of the track re-construction algorithms.

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DISSERTATION
submitted to the
Combined Faculties for the Natural Sciences and Mathematics
of the Ruperto-Carola University of Heidelberg, Germany
for the degree of
doctor rerum naturalium
presented by
Dipl.-Phys. Marc Deissenroth
born in Salzkotten, Germany
stOral examination: April 21 , 2010Software Alignment of
the LHCb Outer Tracker Chambers
Referees: Prof. Dr. Ulrich Uwer
Prof. Dr. Hans-Christian Schultz-CoulonAbstract
This work presents an alignment algorithm that was developed to precisely deter-
mine the positions of the LHCb Outer Tracker detector elements. The algorithm
is based on the reconstruction of tracks and exploits that misalignments of the
detector change the residual between a measured hit and the reconstructed track.
It considers di erent levels of granularities of the Outer Tracker geometry and fully
accounts for correlations of all elements which are imposed by particle trajectories.
In extensive tests, simulated shifts and rotations for di erent levels of the detector
granularity have been used as input to the track reconstruction and alignment
procedure. With about 260 000 tracks the misalignments are recovered with a
statistical precision ofO(10 100m) for the translational degrees of freedom and
2 1ofO(10 10 mrad) for rotations. A study has been performed to determine
the impact of Outer Tracker misalignments on the performance of the track re-
construction algorithms. It shows that the achieved statistical precision does not
decrease the track reconstruction performance in a signi cant way.
During the commissioning of the LHCb detector, cosmic ray muon events have
been collected. The events have been analysed and used for the rst alignment
of the 216 Outer Tracker modules. The module positions have been determined
within 90m.
The developed track based alignment algorithm has demonstrated its reliability
and is one of the core algorithms which are used for the precise determination of
the positions of the LHCb Outer Tracker elements.
Kurzfassung
In der vorliegenden Arbeit wird ein Algorithmus vorgestellt, der entwickelt wurde
um die Positionen der au eren Spurkammern des LHCb Detektors exakt zu be-
stimmen. Der Algorithmus basiert auf der Rekonstruktion von Spuren und nutzt
die Tatsache, da Verschiebungen der Spurkammern das Residuum zwischen einem
Messpunkt und der rekonstruierten Spur verandern.
Der komplexe Aufbau der Spurkammern, bestehend aus verschiedenen Detektorkom-
ponenten, wird berucksichtigt und die durch Spuren hervorgerufenen Korrelationen
zwichen den Komponenten werden berechnet. Umfangreiche Studien haben gezeigt,
da simulierte Verschiebungen des Detektors mit einer statistischen Pr azision von
2 110-100m fur Translationen und 10 -10 mrad fur Rotationen bestimmt werden
konnen (260 000 Spuren).
Der Ein uss von Verschiebungen der au eren Spurkammern auf die Qualit at der
Spurrekonstruktion wurde untersucht. Mit der erreichten statistischen Genauigkeit
sind keine signi kanten E ekte auf die Qualit at der Rekonstruktion zu erwarten.
Waherend der Inbetriebnahme des Detektors wurden Spuren von kosmischen My-
onen aufgenommen. Die Daten wurden analysiert und zur Ausrichtung aller
216 Spurkammern verwendet. Die Positionen der Kammern konnten mit einer
Genauigkeit von 90m bestimmt werden.
Der entwickelte spurbasierte Algorithmus ist einer der Hauptalgorithmen, die
zur prazisen Bestimmung der Positionen der au eren Spurkammern des LHCb
Experimentes verwendet werden.Contents
Introduction 2
1 Theoretical background 3
1.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Quark mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 B meson sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.1 Mixing of B mesons . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.2 CP violation in the B meson system . . . . . . . . . . . . . . . . 10
1.2.3 Rare decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3 B meson production at the LHC . . . . . . . . . . . . . . . . . . . . . . 15
2 The LHCb experiment 19
2.1 Tracking system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1.1 Vertex Locator . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.1.2 Trigger Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.3 Inner Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1.4 Outer Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1.5 Tracking strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2 Particle identi cation system . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.1 Rich Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.2 Calorimeter system . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.3 Muon system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3 Trigger system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.3.1 L0 hardware trigger . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.3.2 High Level Trigger . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4 LHCb software framework . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4.1 Framework applications . . . . . . . . . . . . . . . . . . . . . . 36
3 Impact of misalignments on the track reconstruction 39
3.1 Appliedts and data processing . . . . . . . . . . . . . . . . 40
3.2 Reconstruction performance indicators . . . . . . . . . . . . . . . . . . 41
3.2.1 Tracking e ciencies . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.2 Ghost rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.3 Track Clones . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.4 Event and track weighted quantities . . . . . . . . . . . . . . . . 42
3.3 Track reconstruction performance . . . . . . . . . . . . . . . . . . . . . 43
iii CONTENTS
3.3.1 Forward tracking algorithm . . . . . . . . . . . . . . . . . . . . 43
3.3.2 Track matching . . . . . . . . . . . . . . . . . . . . . 45
3.3.3 Long track algorithm . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3.4 Fit results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4 Alignment - The principles 53
4.1 Introduction to the alignment . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 Intro to the least squares method . . . . . . . . . . . . . . . . . 55
4.3 Determination of misalignment parameters . . . . . . . . . . . . . . . . 56
24.3.1 Global minimization . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.2 Solution of large matrix equations . . . . . . . . . . . . . . . . . 60
4.3.3 Unde ned degrees of freedom . . . . . . . . . . . . . . . . . . . 61
4.3.4 Procedure to constrain unde ned degrees of freedom . . . . . . 62
4.4 Parameterization of the Outer Tracker alignment problem . . . . . . . 65
4.4.1 Misalignment parameters of the Outer Tracker detector . . . . . 65
4.4.2 Unde ned degrees of freedom in the Outer Tracker alignment
procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.4.3 Comparison of two methods to constrain unde ned degrees of
freedom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5 Validation of the LHCb Outer Tracker alignment procedure with sim-
ulated data 75
5.1 Validation procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.1.1 Misaligned Outer Tracker geometries . . . . . . . . . . . . . . . 75
5.1.2 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.1.3 Alignment procedure . . . . . . . . . . . . . . . . . . . . . . . . 79
5.2 Track t of the alignment procedure . . . . . . . . . . . . . . . . . . . . 82
5.2.1 Track model and t procedure . . . . . . . . . . . . . . . . . . . 82
5.2.2 Validation of the track t . . . . . . . . . . . . . . . . . . . . . 84
5.2.3 Ensuring the quality of tracks for the track based alignment . . 86
5.3 Determination of misalignment parameters for half layers without mag-
netic eld . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3.1 Alignment procedure for a singular degree of freedom . . . . . . 88
5.3.2 Alt pro for all geometrical degrees of freedom . . . 93
5.3.3 Track properties after the alignment procedure . . . . . . . . . . 97
5.3.4 Statistical precision of misalignment parameters . . . . . . . . . 98
5.4 Alignment procedure for Outer Tracker modules without magnetic eld 99
5.4.1 Impact of track distribution on the alignment procedure . . . . 101
5.5 Alignment procedure for half layers with magnetic eld . . . . . . . . . 102
5.5.1 Simulated data with magnetic eld . . . . . . . . . . . . . . . . 102
5.5.2 Determination of mislignment parameters . . . . . . . . . . . . 102
5.5.3 Improvement of track properties . . . . . . . . . . . . . . . . . . 103
5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104CONTENTS iii
6 LHCb Outer Tracker alignment with cosmic muons 107
6.1 Cosmic muons in the LHCb detector . . . . . . . . . . . . . . . . . . . 107
6.2 ray muon track reconstruction in the Outer Tracker . . . . . . . 110
6.2.1 Pattern recognition and reconstructed cosmic ray muon tracks . 110
6.2.2 In uence of the pattern recognition algorithm on the alignment
procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.2.3 The origin of multi hit clusters in the Outer Tracker . . . . . . 113
6.3 Alignment procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.4t of half layer positions . . . . . . . . . . . . . . . . . . . . . . 119
6.4.1 Convergence of alignment parameters and track selection . . . . 120
6.4.2 Misalignment parameters for half layers . . . . . . . . . . . . . . 122
6.5 Alignment of module positions . . . . . . . . . . . . . . . . . . . . . . . 124
6.5.1 Correlation of module misalignment parameters . . . . . . . . . 125
6.5.2 Module alignment constants . . . . . . . . . . . . . . . . . . . . 127
6.5.3 Comparison of misalignment parameters obtained for modules
and for half layers . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.5.4 Reproducibility of misalignment parameters . . . . . . . . . . . 132
6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7 Summary and conclusion 135
A Global derivatives 137
B Parameters transformation for Lagrange Multiplier method 139
C Pattern recognition for cosmic muon tracks 140
D Module misalignment parameters determined with cosmic ray data 142
List of Figures 147
List of Tables 151
Bibliography 153

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